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Construction of discrete series for classical $p$-adic groups


Authors: Colette Moeglin and Marko Tadic
Journal: J. Amer. Math. Soc. 15 (2002), 715-786
MSC (1991): Primary 22E50, 22E35; Secondary 11F70, 11S37
DOI: https://doi.org/10.1090/S0894-0347-02-00389-2
Published electronically: April 5, 2002
MathSciNet review: 1896238
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Abstract: The classification of irreducible square integrable representations of classical $p$-adic groups is completed in this paper, under a natural local assumption. Further, this classification gives a parameterization of irreducible tempered representations of these groups. Therefore, it implies a classification of the non-unitary duals of these groups (modulo cuspidal data). The classification of irreducible square integrable representations is directly related to the parameterization of irreducible square integrable representations in terms of dual objects, which is predicted by Langlands program.


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Additional Information

Colette Moeglin
Affiliation: Institut de Mathématiques de Jussieu, CNRS, F-75251 Paris Cedex 05, France
Email: moeglin@math.jussieu.fr

Marko Tadic
Affiliation: Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia
Email: tadic@math.hr

DOI: https://doi.org/10.1090/S0894-0347-02-00389-2
Keywords: Classical groups, $p$-adic fields, irreducible square integrable representations, irreducible tempered representations, non-unitary dual, local Langlands correspondences
Received by editor(s): December 1, 2000
Received by editor(s) in revised form: January 2, 2002
Published electronically: April 5, 2002
Additional Notes: The second author was partly supported by Croatian Ministry of Science and Technology grant # 37001.
Article copyright: © Copyright 2002 American Mathematical Society

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